When I traveled from San Diego > PA..(2945 miles) I really didn't have much with me sadly, it was filled with belongings when I was discharged. Although this is what I would bring along with me... Note I already owned some items, and then I bought things along the way that wasn't because of the road trip.
Inspection Items
Things I own that I didn't buy specifically for a road trip * Since I own a Dewalt 1/2 Impact, I take that with me now with the proper socket for my lug-nuts, 15mm for me at least iirc. * Enough e-juice for vaping along the way for me at-least * Valentine One. Saved my ass a few times going cross country.
Also, water. I know it may get boring after a while driving, but avoid soda as much as you can. Having a sugar high and coming down on a 1k single drive sucks hard.